Zermelo navigation problems on surfaces of revolution and geometric optimal control
B. Bonnard, O. Cots, B. Wembe, ESAIM: Control, Optimisation and Calculus of Variations 29 (2023).
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Journal Article
| Published
| English
Author
Bonnard, Bernard;
Cots, Olivier;
Wembe, Boris
Abstract
<jats:p>In this article, the historical study from Carathéodory-Zermelo about computing the quickest nautical path is generalized to Zermelo navigation problems on surfaces of revolution, in the frame of geometric optimal control. Using the Maximum Principle, we present two methods dedicated to analyzing the geodesic flow and to compute the conjugate and cut loci. We apply these calculations to investigate case studies related to applications in hydrodynamics, space mechanics and geometry.</jats:p>
Publishing Year
Journal Title
ESAIM: Control, Optimisation and Calculus of Variations
Volume
29
Article Number
60
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Cite this
Bonnard B, Cots O, Wembe B. Zermelo navigation problems on surfaces of revolution and geometric optimal control. ESAIM: Control, Optimisation and Calculus of Variations. 2023;29. doi:10.1051/cocv/2023052
Bonnard, B., Cots, O., & Wembe, B. (2023). Zermelo navigation problems on surfaces of revolution and geometric optimal control. ESAIM: Control, Optimisation and Calculus of Variations, 29, Article 60. https://doi.org/10.1051/cocv/2023052
@article{Bonnard_Cots_Wembe_2023, title={Zermelo navigation problems on surfaces of revolution and geometric optimal control}, volume={29}, DOI={10.1051/cocv/2023052}, number={60}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, publisher={EDP Sciences}, author={Bonnard, Bernard and Cots, Olivier and Wembe, Boris}, year={2023} }
Bonnard, Bernard, Olivier Cots, and Boris Wembe. “Zermelo Navigation Problems on Surfaces of Revolution and Geometric Optimal Control.” ESAIM: Control, Optimisation and Calculus of Variations 29 (2023). https://doi.org/10.1051/cocv/2023052.
B. Bonnard, O. Cots, and B. Wembe, “Zermelo navigation problems on surfaces of revolution and geometric optimal control,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 29, Art. no. 60, 2023, doi: 10.1051/cocv/2023052.
Bonnard, Bernard, et al. “Zermelo Navigation Problems on Surfaces of Revolution and Geometric Optimal Control.” ESAIM: Control, Optimisation and Calculus of Variations, vol. 29, 60, EDP Sciences, 2023, doi:10.1051/cocv/2023052.
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